In this paper we try to understand the heuristics that underlie the decisions made by the Horn query learning algorithm proposed in [1]. We take advantage of our explicit representation of such heuristics
in order to present an alternative termination proof for the algorithm, as well as to justify its decisions by showing that they always guarantee that the negative examples in the sequence maintained by the algorithm violate different clauses in the target formula. Finally, we propose a new
algorithm that allows multiple refinement when we can prove that such a refinement does not affect the independence of the negative examples in the sequence maintained by the algorithm.